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Proof step 9 from proof sgn-mklist-03 (previous step)

mklist(boolvar, m).first ↔ boolvar, ∀ boolvar. sgn(mklist(boolvar, m)) = boolvar ' ⊦ sgn(mklist(boolvar, m)) = boolvar ', m = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [mklist(boolvar, m), boolvar0, bits] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: ⊦ mklist(boolvar, m) = [] ↔ m = 0;%bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: mklist(boolvar, m), boolvar0, bits